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The R3- allotrope: a pathway towards under high SUBJECT AREAS: MECHANICAL pressure PROPERTIES ELECTRONIC MATERIALS Xue Jiang1,2, Cecilia A˚ rhammar3, Peng Liu1, Jijun Zhao2 & Rajeev Ahuja1,4 STRUCTURE OF SOLIDS AND LIQUIDS 1Department of Materials and Engineering, Royal Institute of Technology, 10044 Stockholm, Sweden, 2Key Laboratory of Materials ELECTRONIC STRUCTURE Modification by Laser, Ion and Electron Beams Dalian University of Technology, Ministry of Education, Dalian 116024, China, 3Sandvik Coromant, Lerkrogsv. 13, S-126 80 Stockholm, Sweden, 4Department of Physics and Astronomy, Box 516, Uppsala University, 75120, Uppsala, Sweden. Received 8 November 2012 Pressure-induced bond type switching and phase transformation in glassy carbon (GC) has been simulated Accepted by means of Density Functional Theory (DFT) calculations and the Stochastic method (SQ) in a 25 April 2013 wide range of pressures (0–79 GPa). Under pressure, the GC experiences a hardening transition from sp- and sp2-type to sp3-type bonding, in agreement with previous experimental results. Moreover, a new Published crystalline carbon allotrope possessing R3 symmetry (R3-carbon) is predicted using the stochastic SQ 23 May 2013 method. The results indicate that R3-carbon can be regarded as an allotrope similar to that of amorphous GC. A very small difference in the heat of formation and the coherence of the radial and angular distribution functions of GC and the R3-carbon structure imply that small perturbations to this crystalline carbon Correspondence and allotrope may provide another possible amorphization pathway of carbon besides that of quenching the liquid melt or gas by ultra-fast cooling. requests for materials should be addressed to J.Z. ([email protected]. arbon is an intriguing element for scientists from many fields because of the diverse sp, sp2 and sp3 bonding cn) or R.A. (rajeev. states and its fascinating physical and chemical properties1. Within condensed matter physics, there are [email protected]) many well-known carbon allotropes, namely; , , , nanotubes, and C 2–4 . Motivated by the supreme properties and potential applications of those carbon structures, there is great interest in synthesizing new allotropes. The term glassy carbon (GC) includes numerous modifications of carbon with different fraction of sp, sp2 and sp3 hybridized states from short-range to intermediate-range-order structures. Many of these modifications are used within industrial applications where their unique properties are utilized. Combining the chemical inertness of a with the high electrical conductivity of a ceramic, GC finds important applications in the manufacturing of crucibles and electrodes and as coatings for electronic devices. One commonly used thin film form of glassy carbon is the diamond like carbon coating, which is well used as a protective wear resistant coating. Within this group of glassy carbon coatings, some contain about 50 at.% (a-C:H), other contain less than 1% hydrogen (a-C)5. The a-C:H typically contain sp3 fractions smaller than 50%, while the a-C films can contain 85% or more sp3 bonds5. Many different structures of glassy carbon have been suggested on the basis of X-ray Diffraction (XRD)- measurements and the high resolution transmission electron microscopy imaging4. Ergun and Tiensuu2 found both sp2 and sp3 C-C bonds in glassy carbon. Jenkins3 considered the GC crystallite as a complex -like structure, where graphite-like layers were stacked together. The model of glassy carbon with carbyne-like chains has also been proposed by Pesin et al.5. Recently, a model for the structure of glassy carbon at high and low temperature have gained acceptance6. The high temperature structure can be thought of as mainly consisting of broken or imperfect fullerene-like multilayered nanoparticles with very large enclosed pores. The low temper- ature structure consists of a curved carbon sheet consisting of pentagons, heptagons and hexagons. The transformation mechanism amongst various forms of carbon allotropes and the unrevealed metastable phases along these transition pathways have been a long-lasting issue, since these polymorphs possess entirely different electronic and mechanical properties. Cold compression with diamond anvil cell (DAC) and first- principles simulations are regarded as the most powerful experimental and theoretical tools to interpret the process of conversion7. At hydrostatic pressure up to 5 GPa, many experiments reveal a fascinating phase transformation of into ordered or disordered diamond or graphite8, in which the hardness sometimes

SCIENTIFIC REPORTS | 3 : 1877 | DOI: 10.1038/srep01877 1 www.nature.com/scientificreports can approach that of perfect sp3-type diamond. Moreover, the com- pression behavior, the phase diagram, the optical, electronic, and mechanical properties of the C60 have been well investigated in the past decade9. By means of cold compression of graphite at ambient temperature, Mao et al.7 observed partial sp2-type bonds conversion into sp3-type bonds in graphite at around 14 GPa, which demonstrated the formation of a new superhard phase instead of the hexagonal and cubic . Theoretical studies have proposed several possible structures for such cold compressed graphite, includ- ing the monoclinic M carbon10, body centered tetragonal Bct-C4 carbon11, orthorhombic W carbon12, R carbon, P carbon13, and Cco-C8 carbon14. The XRD-patterns of those predicted structures showed a rough agreement with the corresponding experimental results, However, M-Carbon has been recently supported again by experiment15. With the aid of high temperature (T 5 2300–2500 K), graphite converts completely into diamond at pressures above 15 GPa16,17. Very recently, Lin et al.18 observed a new carbon allo- trope with a fully sp3-bonded amorphous structure formed from GC Figure 1 | The cohesive energies and symmetries of twenty random carbon structures with the densities of graphite (2.24 g/cm3) and after hydrostatic loading of more than 40 GPa at room temperature. 3 Using synchrotron X-ray , they found a con- diamond (3.52 g/cm ), respectively. tinuous pressure-induced sp2-to-sp3 structural change. This new GC allotrope was suggested to be a superhard material, as indicated by its of R3, it is clear that the R3-structure has its main peaks at 24.1 and exceptional yield strength up to 130 GPa with a confining pressure of 36.4 degrees 2h, angles at which no other of the compressed graphite 60 GPa. Yet the exact glassy carbon structures during phase trans- phases display any diffracted peaks. Moreover, all other carbon allo- ition and the origin of its superior mechanical properties has not tropes display main peaks between 40 and 45 degrees 2h, whereas been explained. R3-carbon completely lacks intensity in this region. In this paper, we explore the detailed structures of GC and illus- In order to investigate the dynamical stability of the R3-phase, trate its mechanical properties under a wide pressure range of 0– phonon dispersion relationships have been calculated by Density 79 GPa by means of DFT. The initial GC model at ambient pressure Functional Perturbation Theory (DFPT) and the code of Phonopy was built by the stochastic quenching (SQ) method19–23 where the (Fig. 3). The Brilliouin zone of this allotrope is complex due to its low density and minimum number of carbon were tested carefully. symmetry and therefore phonon frequencies along paths in all three Our results provide theoretical evidence of a change in bonding type directions in space were studied (G-A-H-K-G-M-L-H). From the (sp, sp2, and sp3) of the GC-structures under high pressure. A certain calculated phonon spectrum it is clear that there are no negative amount of the C2 dimer was found in the glassy carbon structures, frequencies throughout the entire Brilliouin zone, which confirms independently of the loading pressure but decreasing with annealing that the R3-phase is dynamically stable. 2 3 temperature. The existence of the C2-dimer may delay the sp -sp We first performed benchmark testing of the SQ method for a 4- transformation. More strikingly, we predict a new carbon crystalline atoms and a 8-atoms cell with densities of 2.24 g/cm3 and 3.52 g/cm3, phase which can be triggered to transform into the amorphous state respectively, corresponding to the density of graphite and diamond. by exerting a small perturbation to the system. It can be regarded as To assess the accuracy of our first-principles total energy methods, we the embryo of GC and may provide an alternate method of amor- calculated the lattice constants and cohesive energies of diamond and phization of the carbon phase besides quenching from liquid melt or graphite using three exchange correlation functionals: the gas by ultra-fast cooling. Perdew-Becke-Ernzerhof functional for solids and surfaces (PBEsol), a density functional constructed with a long-range disper- Results sion correction (D2)25 and the van der Waals density functional 26 Figure 1 shows the cohesive energies and symmetries of twenty ran- (vdW-DF) . In the bulk calculations, the Brillouin zone was sampled dom structures generated by the SQ method. Clearly, these twenty by a 10 3 10 3 10 k points mesh. The computed results are com- structures cover many different atomic arrangement and symmet- pared with experimental values in Table I. For the lattice constants, ries. As already demonstrated in our previous work24, the SQ method the results of DFT-D2 method shows best agreement with the experi- efficiently reproduces metastable phases that may only be found mental values, while the vdW-DF method yields the largest error bars. experimentally by ultrafast cooling from liquid melt or by off- This sequence is completely opposite for the cohesive energy, where equilibrium synthesis. In addition, beyond the previously reported the error decreases in the order DFT-D2, DFT/PBEsol and vdW-DF. stable or metastable carbon phases (cubic diamond, monoclinic M- Moreover, the description of lattice constants and cohesive energy carbon10, body centered tetragonal bct-C4 carbon11, orthorhombic using vdW-DF method is comparable to previous calculations27. W carbon12, R carbon, P carbon13 and Cco-C8 carbon14), our simula- Considering the accuracy in the calculation of structures and cohesive tions reveal a new trigonal structure with R3 symmetry. In Figure 2 energies as well as the computational time, we chose the PBEsol (a) the detailed structure of this phase which we denote the R3- functional for the rest of all first-principles calculations in this paper. carbon phase is displayed. Within the unit cell of this structure, there The validity of our glassy carbon model structure was assessed by are four inequivalent atoms bound with sp3 hybridized covalent computing the energy and total density of states (TDOS) of glassy bonds. The calculated atomic density and band gap are slightly lower carbon supercell models with different number of carbon atoms than that of diamond. The calculated XRD-patterns of the R3-carbon (100, 150, and 200 atoms). As shown in Figure 4a and its inset table, phase along with the other carbon allotropes studied in this paper are the total energy and the fingerprint peaks of TDOS converge at a shown in Figure 2 (b). R3-carbon phase is markedly different from S supercell size of 150 atoms, further increasing the number of atoms in and B families of cold compressed graphite as is defined by Niu the GC model does not significantly change the total energy per et al.17. The R3-carbon contains three-membered rings which enable carbon and the principal shape of TDOS. Previous studies have a more compressed structure and serve as binding blocks between demonstrated that the supercell sizes of 150–200 atoms were enough five and eight membered rings. Studying the calculated XRD-pattern for those amorphous phase investigations19,20,23,24. The total energy as

SCIENTIFIC REPORTS | 3 : 1877 | DOI: 10.1038/srep01877 2 www.nature.com/scientificreports

Figure 2 | (a) The R3-structure, the (001)-plane and the (010)-plane. Three-membered rings are colored in purple. (b) The calculated diffraction pattern of the R3 phase, Cco-C8 Carbon, Bct-Carbon, M-Carbon, Z-Carbon, P-Carbon, R-Carbon, S-Carbon, T-Carbon, W-Carbon and X-Carbon, respectively. a function of density (or volume) of the 150 atoms GC structure is chain segments that interlink to form some curved fragments of non- plotted in Figure 4b. There is a local minimum in the total energy at a classical fullerenes, which include three-, four-, five-, six-, seven-, and density of 1.88 g/cm3. Therefore, the dimension of the 150-atom eight- membered rings incorporating a very high sp2 ratio (90%). 2 supercell for the ground-state GC was fixed to be 14.41 A˚ (corres- These sp fullerene fragments are stabilized by p bonding (C2 dimer). ponding to a density of 1.88 g/cm3), respectively, which is within the Moreover, there also exist sp3 hybridized atoms interlinking the sp2 range of the experimental densities for GC (1.02 g/cm3 to 2.1 6 1g/ dominated fullerene fragments, but the content is quite low. The cm328) and agrees with the previous finding that the density of GC is binding type and relative content of bonding states of GC obtained lower than that of pure graphite (2.24 g/cm3)4. by our stochastic quenching method are comparable to previous Overall speaking, the SQ method is able to locate a large number of theoretical structural models2,3,5,6. possible metastable carbon allotropes with either sp2 or sp3-type Figure 5 shows the representative GC structures under different bonding, which have been previously found by other random struc- external pressures of 0 GPa, 3.6 GPa, and 56 GPa, respectively. In tural searches10–12,14 in a satisfactory manner. The ground-state general, these structures show distinct differences. For example, GC graphite structure seems not reachable using this method without below 0 GPa has a two dimensional (2D) layered structure, while GC applying any symmetry constraint. This result differs from that between 0 and 56 GPa exhibits a compact, three dimensional cross- found for monoatomic by Holmstro¨m et al.20, who found that linked network. Under compression, there is a clear tendency of the global energy minimum of the crystalline could be obtained increased density and the CN, as shown in Table II. Up to a high for a small enough size of the cell. We attribute this difference firstly pressure of 79 GPa, the density rises to 3.75 g/cm3, which is even to the use of a cubic cell for the random guess and to the covalent higher than for the ambient diamond (3.35 g/cm3). Moreover, the CN nature of C-C bonds as well as the stronger tendency for carbon to is also close to the maximal coordinate number of sp3 carbon, i.e. 4. amorphize compared to simple monoatomic metals. Nevertheless, it To gain deeper insight into the relationship between the detailed is reasonable to use the SQ-method for mapping the potential energy structures and static pressures, the evolution of local atomic struc- landscape of a disordered phase such as glassy carbon, as was also tures of GC as a function of pressure can be monitored by the bond demonstrated in our previous paper24. length and bonding states of C-C (dimer, sp, sp2 and sp3). Figure 6 and We further investigated the structural changes of GC under a Table II show the bond length and fraction of sp, sp2, and sp3 in the series of hydrostatic pressures. The pressures were gradually applied static pressure range of 0–79 GPa. Upon compression, the variation as follows: the target volume was fixed to a certain value, and the cell of bond length can be divided into three distinct regions. From a to b geometry and atomic positions were relaxed simultaneously to (0–3.65 GPa), the bond length remains nearly invariant, the ratio of obtain the final structures. We reduced the desired target volume sp and sp2 decreases very slowly, and the sp3 content only increases step by step and repeated the above procedure until the external from 7% to 11%. These results imply that the compression process of pressure reached 79 GPa. We first analyzed the structural character- the broken or imperfect graphitic layer progressively approaches istics of GC at ambient pressure, as presented in Table II. For the each other but does not reach the characteristic distance of C-C initial GC at ambient pressure, the density (r) is 1.88 g/cm3 and the bonding. The region from b to c corresponds to a pressure range of mean coordination number (CN) is 2.8, both are lower than r 5 3.65–9.86 GPa, where the fraction of sp3 type bonding increases 2.24 g/cm3 and CN 5 3 of graphite. With such low density and small sharply. Meanwhile, the sp bonding vanishes gradually and the ratio coordination number, a 3-D network structure is still not achieved. of sp2-type bonding also reduces to nearly 40%. At a pressure of Thus, the ground state structure of GC is composed of sp-hybridized 9.86 GPa, the ratio of sp3 carbon (42%) is comparable to that of sp2

SCIENTIFIC REPORTS | 3 : 1877 | DOI: 10.1038/srep01877 3 www.nature.com/scientificreports

pressure is less than 10 GPa, pressure-induced rehybridization from sp2 to sp3 dominates, and thus the C-C bond lengths are elongated31. This is a consequence of the formation of tetrahedral sp3 bonds through removing the unsaturated antibonding states of carbon, as is illustrated in Figure 7. C_p unsaturated bonds at the Fermi level as well as high energy antibonding states are prominent in the unpres- surized structure. As the structure is gradually pressurized both these features diminish (Fig. 7). As a reference, the typical bond length of sp3 hybridized carbon is 1.54 A˚ (diamond), while 1.42 A˚ is the length of the s-bond length in graphite31. Above 10 GPa, the sp3-hybridized carbon is more favorable in the amorphous structure, but the pres- sure-induced shrinking of the bond length is more pronounced. As a consequence, the bond lengths in all the structures under different pressures are all smaller than the standard C-C sp3 bond length, 32 namely, 1.54 A˚ . This can be understood from the presence of C2 dimers, which we will discuss in the following. Interestingly, up to a pressure of 79 GPa and a density of 3.65 g/cm3 we observed a certain number of C2 dimers in the GC, which are formed as a result of the p- Figure 3 | The calculated phonon spectrum of the R3 phase along some interaction where triple like bonds of about 1.23 A˚ length are 33 selected paths in the Brillouin zone. formed . With increasing pressure, those C2 dimers do not vanish, that is, the density of the C2 dimers is not sensitive to the loading carbon (49%) and sp2 hybridized 2-D graphite-like structures trans- pressure on the GC. For example, the concentrations of the C2 dimer form to sp3 diamond-like ones. The loss of half of the p-bonds can be in the GC structures under pressures of 0 GPa, 6.56 GPa, 18.49 GPa, explained by the formation s-bonds between imperfect graphitic 55.9 GPa, and 79 GPa are 9%, 12%, 11%, 13% and 11%, respectively. layers as the layers continue to approach each other. Under further In Figure 8, the simulated XRD-patterns for the GC at different compression (the third region from c to d), the 2-D carbon sheets pressures are presented and compared with the experimental data measured by Lin et al.18 under an external pressure of 45.4 GPa. To begin to deeper bend and further hybridize with each other. ˚ Therefore, the bonding states convert sequentially; as the pressure generate the simulated XRD-pattern, a wavelength of l 5 0.3982 A becomes larger than 50 GPa, the original sp2 type carbon totally was used. Two peaks resembling the (002) interlayer distance and the convert to sp3 type. (100) intralayer distance (and higher index planes) of polycrystalline 3 graphite are found. The distance between these peaks stays rather The variation in sp fraction with pressure is compared to the ˚ ˚ calculated sp3 fractions in structures of amorphous carbon generated constant, from 2.92 A (0 GPa) to 3.11 A (79 GPa) and Comparable 18 ˚ by the Car-Parrinello method and by the environment-dependent to that of Lin et al. of 2.80 A (45.4 GPa). The reduction in inter- planar spacing (d) and the large pressure-induced shift of the peak interaction potential (EDIP) developed by Marks et al.29,30. In their 64 corresponding to the distance between the soft (002) interlayers are atom simulations, they found a sp3 fraction of 57% at a density of also reproduced. However, the relative peak intensities do not com- 2.9 g/cm3, which should be compared to our calculated sp3 fraction of pare well with Lin et al.18 and the low angle peak which appears at 45% at density of 2.89 g/cm3. Assuming that the fraction of dimers around 5.5 degrees 2h in Lin’s XRD-pattern is not reproduced. In our generated in the SQ method at this density (11%) would transform to calculated XRD-spectra, the shift of the (002)-peak, corresponding to sp3-like bonds as the structure is allowed to equilibrate at sufficient the decrease in interlayer distance is largest up to 30.3 GPa and seems temperature, the sp3 content from our model will increase to 56% to be related to the formation of a 3D-network. Above this threshold, which is in close agreement with the results by Marks et al.29,30. there is no significant change of interlayer distance; instead splitting Moreover, Marks et al.29,30 also found that the sp3 content would of both peaks occurs, indicating further symmetry breaking. The increase with increasing time of thermalization. agreement with Lin et al. is overall relatively poor, suggesting that The variation of bond length of GC can be understood by the the GC allotrope found by the SQ-method is different to that syn- following two competing effects: high-pressure compression (which thesized by Lin et al.18. tends to shrinks the bond length) and the interconversion from sp2 to Our result deviates from the experimental findings by Lin et al.18 in sp3 hybridization (which results in longer C-C bond length). As the two major aspects: (A) we find a considerably higher transition pres- sure, or rather, we do not find a complete sp2 to sp3-transformation; (B) we find C-C dimers, which display some p-bonding for all the Table I | The lattice constants and cohesive energies of graphite pressures investigated in this work. Indeed, the occurrence of C and diamond computed by different exchange correlation func- 2 dimers in our amorphous carbon structures is still reasonable, since tionals, including the Perdew-Becke-Ernzerhof functional for solids the C2 dimer is also believed to be an important species or even a and surfaces (DFT/PBEsol), density functional constructed with a nucleation centre for the growth of diamond or nanotubes in experi- long-range dispersion correction (DFT-D2) and the van der ments34,35. The existence of dimers is one of the reasons to why we do Waals density functional (vdW-DF), compared with the relevant not obtain a 100% sp3 bond amorphous GC allotrope. One important 31 experimental data . (The c/a ratio of graphite is set to 2.76 in cause of the difference between our calculated GC and the structure present calculations) found by Lin et al.18 might be the synthesis method of the GC, which 18 Graphite PBEsol vdW-DF DFT-D2 Expt. was not specified in the letter by Lin et al. . The SQ-method does, as pointed out previously, well describe highly metastable structures ˚ a(A) 2.458 2.465 2.460 2.460 formed in non-equilibrium processes, such as plasma-enhanced EC(eV) 8.29 7.99 8.41 7.37 chemical vapor deposition or physical vapor deposition of thin films. 18 Diamond PBEsol vdW DFT-D2 Expt. Lin et al. instead uses a small bulk sample. Moreover, the temper- ˚ ature may also be an important parameter to consider. Therefore, a(A) 3.554 3.574 3.545 3.54 MD simulations at 300 K, 700 K and 1300 K were performed for two E (eV) 8.28 7.88 8.49 7.58 C of the high pressure GC phases (56 GPa and 79 GPa). The fraction of

SCIENTIFIC REPORTS | 3 : 1877 | DOI: 10.1038/srep01877 4 www.nature.com/scientificreports

Figure 4 | (a) Total density of state for increasing number of carbon atoms in the GC structure. The insert table displays the relationship between total energy with different density and number of carbon atoms in the model (b) The total as a function of density density of GC with 150 carbon atoms. each bond type before and after heating is shown in Table III. We than graphite. More importantly, one can clearly see that the energy found the pairs of C2 dimers decreasing from 13 to 4 and from 11 to 1, of GC under some pressures lies only 0.2 eV/atom above than R3- respectively, when increasing temperature from 0 K to 1300 K. carbon. Such a small energy difference suggests a possible transition This suggests the C2 dimers would be considerably decreased in between them. However, to accurately consider also the kinetics of amount or dismissed if the experiments were performed at a high this transition, calculation of activation energy barriers for the dif- temperature. fusion of carbon from ideal sites in the crystalline R3-structure to the The thermodynamical stability, excluding the contribution from distorted positions of the GC-structure is required. vibrational and mixing entropy, of pressure-induced GC can be We now turn to explore the structural correlation between GC and determined by calculating the enthalpies H 5 E 1 PV, where E is R3-carbon, Figure 10 displays the structures of GC under three dif- the internal energy, P is the applied pressure, and V is the volume, ferent pressures (8.46 GPa, 30.3 GPa and 58.3 GPa). After carefully without considering temperature. After optimizing the structures of analyzing the structures, we however found a very high content GC under pressure, the value of the enthalpies can be obtained. The (around 10%) of a unit, similar to that of R3-carbon (or early phase). relationship between the calculated enthalpies and pressures for The early phase resembles crystalline R3-carbon but with distorted these pressure-dependent GCs in comparison with our calculated atomic positions or disconnecting one of the C-C bonds. As is seen in value of some crystalline phases (diamond, graphite, T-carbon, M- Figure 10, the early phase of GC contains three-membered carbon carbon, W-carbon, R3-carbon, Bct-C4 carbon, and Cco-C8 carbon) rings acting as building blocks between 5 and 8-membered rings, in are plotted in Figure 9. According to the computed enthalpy, at proximity with R3-carbon. It is of interest to examine the radial 0 GPa GC is 0.5–1 eV less stable than some of the crystalline phases distribution function (RDF) and angular distribution function (diamond, graphite, M-carbon, W-carbon, R3-carbon, Bct-C4 car- (ADF) to further discuss the structural similarities, which are shown bon, Cco-C8 carbon); however, it is more stable than T-carbon. in Figure 11. These will describe the local order and orientation of Under compression, M-carbon, W-carbon, Bct-C4 carbon, and carbon in the GCs, and is therefore better tool than XRD patterns. At Cco-C8 carbon become more stable than graphite beyond pressures a first glance, all three representative GC structures exhibit obviously of 15–25 GPa, which are comparable to the predictions made by amorphous features and the first nearest neighbor distance and sec- many other groups10–12,14. In previous works, these phases were con- ond nearest neighbor distance of the RDF from our simulations are sidered as the main products of cold compression of graphite. The about 1.47 and 2.47 A˚ . Both the positions are consistent with the R3-phase and glassy carbon display higher enthalpies (less negative) previous experimental36 and theoretical papers29,30. From ADF, we

Table II | Structural data for the GC under different pressures as calculated in this work, including mass density (density), the ratio of the C2 2 3 dimer, twofold coordinated atoms (sp), threefold coordinated atoms (sp ), threefold coordinated atoms (sp ), mean bond length (R1), average total coordination number (CN), bulk modulus (B), shear modulus (G) and Young’s modulus (E). The theoretical results of bulk diamond are also shown for comparison

3 2 3 ˚ Pressure (GPa) Density (g/cm )C2 dimer (%) sp (%) sp (%) sp (%) R1 (A) CN B (GPa) G (GPa) E (GPa) 0 1.88 9 12 72 7 1.463 2.86 97 36 96 3.61 2.09 9 10 70 11 1.462 2.95 111 62 156 6.56 2.35 12 3 60 25 1.470 3.10 138 87 216 8.46 2.50 13 0 53 34 1.476 3.23 150 101 248 9.86 2.68 9 0 49 42 1.496 3.43 240 154 381 18.49 2.89 11 0 44 45 1.488 3.4 256 152 389 30.3 3.13 15 0 32 53 1.485 3.49 315 215 525 55.9 3.48 13 0 12 75 1.48 3.7 416 270 666 58.3 3.54 13 0 9 78 1.48 3.72 434 314 759 79 3.75 11 0 0 89 1.475 3.78 521 368 893 diamond 3.52 0 0 0 100 1.54 4 447 540 1159

SCIENTIFIC REPORTS | 3 : 1877 | DOI: 10.1038/srep01877 5 www.nature.com/scientificreports

Figure 5 | The GC structures under different pressure (0 GPa, 3.6 GPa, and 56 GPa). The red carbon pairs represent the C2 dimer. can clearly see there are four distinct peaks located at about 60u,90u, concentration. Especially, there are many four coordinate covalent 109u, 120u and 140u in the R3 structure. The 60u peak corresponds to systems observed where an order to disorder crystal to amorphous the internal angles in the three-membered rings, whereas the 90u transition occurs. The instability of the diamond structure caused peak is attributed to bonds between these rings and the five- and by phonon softening under compression may also lead to the 42 eight-membered rings. 135u is the internal angle of an ideal octagon. transformation into the disordered state . More interestingly, C60 In the R3-carbon the octagons are buckled, giving rise to peak con- fullerene under heating at moderate pressures will transform to the tributions between 105 and 140u. Finally, the 109u peak corresponds hard amorphous state, which is a similar case to our GC43. to the dominant angle of sp3-hybridized carbon. From the calculated Commonly, solid state amorphization happen due to two basic fea- RDF, ADF and XRD-pattern of R3 we can conclude that such an tures: a deep metastability of initial crystal and a similarity between unusual topology has not been reported for cold compressed graph- the short-range order structures of the initial crystalline and final ite before and, furthermore, we find that characteristic peaks and amorphous phase. Thus, based on our energetic analysis, RDF and characteristic Angles also exist in the GC structures under different ADF simulations, we can infer that by exerting some kind of per- pressure (8.46 GPa, 30.3 GPa, 58.3 GPa), which verify a similarity turbation (temperature, pressure, displacement, laser, ion bombard- between the short-range order structures of the R3-carbon crystalline ment, etc) on the crystalline R3-carbon, the long-range order may and the final glassy carbon phase. collapse and thus GC can be generated. Therefore, both a small energy difference and the close similarity For sp3-carbon rich systems, the most important applications are of GC and the R3-carbon structure mentioned above suggests that their excellent mechanical properties inherited from diamond. Based the synthesis of GC from the R3-phase might be another route to on the equilibrium structures, we evaluated the mechanical prop- produce the amorphous phase of carbon via a solid state amorphiza- erties of these GCs under different pressures. The bulk moduli, shear tion (SSA). This phase transformation is different from the liquid to solid or gas to solid transition which both are generated by quenching the liquid melt or gas by ultra-fast cooling, accompanied by signifi- cant change of structures37,38. SSA has been investigated by several studies reports39–43. Cahn and Johnson39 suggested SSA is a first-order phase transformation which can be caused by different driving forces, such as , high energy particle irradiation, chemical diffusion, temperature or pressure. For example, Rehn et al.40 indicated that SSA was triggered by an elastic instability. Fecht41 also established a general theory for crystal- transitions and demonstrated that the crys- talline phase can be ‘melted’ by a discontinuous increase of vacancy

Figure 6 | The ratio of sp2 and sp3-type carbon bonding and bond length Figure 7 | The evolution of orbital-projected density of states of the GC of GC with respect to external pressure up to 80 GPa. structure with pressure. The Fermi level is set to 0 eV.

SCIENTIFIC REPORTS | 3 : 1877 | DOI: 10.1038/srep01877 6 www.nature.com/scientificreports

Table III | Structural data for the GC under 56 GPa and 79 GPa from MD simulations at 0 K, 300 K, 700 K, 1300 K, including the ratio of the C2 dimer, twofold coordinated atoms (sp), twofold coordinated atoms (sp2), and threefold coordinated atoms (sp3)

2 3 Pressure (GPa) T (K) C2 dimer (%) sp (%) sp (%) sp (%) 56 0 13 0 12 75 300 8 0 9 83 700 4 0 6 90 1300 4 0 5 91 79 0 11 0 0 89 300 3 0 2 95 700 0 0 3 97 1300 1 0 3 96

Young’s modulus rises gradually. As the pressure reaches 79 GPa, the content of sp3 bonding state reaches 90%, and the bulk moduli, shear moduli, and Young’s moduli become 521 GPa, 368 GPa and 893 GPa, respectively. In our previous works45,46, we found Young’s modulus a quite reliable parameter for estimating Vickers hardness of common covalent materials. If so, the pressure-induced GC struc- tures are anticipated to possess a hardness approaching that of Diamond.

Discussion In summary, we successfully generated one local minimum GC Figure 8 | XRD-patterns of GC at different pressures compared with structure among a series of random structures with the SQ method. experimental data taken from Ref. 18. By means of DFT calculations we analyzed in detail its structural, thermodynamic and mechanical properties in a wide range of pres- moduli, and Young’s moduli of the GC under different pressures sures (0–79 GPa). We present a theoretical picture of the pressure- from our calculations are listed in Table II. For comparison, the induced phase transformation in GC, in proximity with previous elastic constant of diamond is also calculated using the same scheme. experimental results. The transition pressure and obtained structure The calculated bulk, shear modulus and Young’s modulus of will depend on the specific synthesis method of the GC. The static 447 GPa, 540 GPa and 1159 GPa for diamond crystal are in good pressure results in bond length changes and in a transition from sp to agreement with the experimental values of 442 GPa, 540 GPa and sp2 and sp3 carbon bonding states for GC. Consequently, the mech- 1205 GPa44, respectively. Obviously, the bulk, shear, and Young’s anical properties significantly vary due to the change of bonding moduli of GC are strongly affected by the fraction of different bond- type. With increasing pressure, the bulk moduli, shear moduli ing states. With increasing content of sp3 carbon bonding state, the and Young’s moduli approach diamond values. This may be an

Figure 9 | Enthalpy of formation calculated for different carbon allotropes (diamond, graphite, M-carbon, W-carbon, R3-carbon, Bct-C4 carbon, Cco-C8 carbon, T-carbon and GC) for pressures up to 60 GPa.

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Figure 10 | Other possible transition paths from crystalline to amorphous carbon instead of quenching from liquid. The R3-carbon structure can be seen as an initial unit of GC. (a) The primitive cell, supercell structure and atomic positions of the R3-crystalline carbon allotrope with trigonal symmetry of R3. (b) The structure of GC under different pressure (8.46 GPa, 30.3 GPa and 58.3 GPa). The cluster composed of purple carbon atoms is some representative units of the distorted R3-carbon. indication that off-equilibrium synthesis of glassy-carbon in bulk or by ultra-fast cooling. This structure might also be tested as a seed thin film form, at high enough pressures may well result in a func- layer for ‘‘epitaxial’’ growth of GC, utilizing their close-lying local tional bulk material or coating with a hardness approaching that of structure and energetics. Therefore, we anticipate that the novel diamond. crystalline carbon allotrope and the promising pathway from this In addition, our results predict a new crystalline carbon allotrope allotrope to synthesize amorphous carbon can be validated by future named R3-carbon. Both the heat of formation and similar short- experiments. range order structures of R3-carbon and GC infer that this phase can be regarded as the embryo of amorphous GC. It provides another Methods pathway to amorphization besides quenching from liquid melt or gas In the present simulation, the ground state GC structures were generated by the stochastic quenching (SQ) method19–23, utilizing density functional theory (DFT) as implemented in the VASP package47. In our previous study of amorphous metal oxides by ultra-fast cooling from gas phase, it was shown that the SQ method provides 24 a good description of the potential landscape of amorphous Al2O3 . Initially, the atoms are distributed randomly within the simulation box, which in this case was a cubic supercell, where after the atomic positions were allowed to relax by the con- jugate gradient method. The projector augmented wave (PAW) method48 was adopted and the 2s22p3 electrons of C were treated as valence electrons. A high energy cutoff of 700 eV was used for the plane-wave basis to ensure good convergence of the total energy and stress. The exchange-correlation interaction was described by the Perdew-Becke-Ernzerhofer functional (PBE) developed for solids and surfaces (PBEsol)49 within the gradient generalized approximation (GGA). The Brillouin zone was sampled in the C point only for the 150 atoms supercell of GC. During the relaxation process, we fixed the supercell geometry and turned the symmetry off. To ensure the reliability of the SQ method, we quenched 20 different random config- urations with the density of graphite (2.24 g/cm3) and diamond (3.52 g/cm3), respectively. The volume and number of carbon atoms in the simulation cell were also determined carefully by repeating the above procedure. The final structures obtained at different pressures were further optimized using higher cutoff of 1000 eV in order to evaluate the mechanical properties accurately. For the quasi-cubic supercell, the bulk modulus (B) was directly fitted from the derivative of Pressure–Volume (P–V) relationship under hydrostatic compression. Using the finite strain method50, we computed the elastic constants of the quasi-cubic supercell and then evaluated the isotropic shear modulus (G) using the Voigt–Reuss– Hill average scheme51. Consequently, the isotropic Young’s modulus (E) can be calculated using the relationship: E 5 9KG/(3K 1 G). The dynamical stability of R3-carbon was investigated by phonon calculations in the software Phonopy52. The Perdew Becke Ernzerhof-functional (PBE)53, a k-point mesh of 6 3 6 3 6 k-points, centered in the G-point and a cutoff of 750 eV, with the energy convergence limit of 1028 eV was used to accurately relax the unit cell con- sisting of 24 atoms. The force constants were calculated in real space, within Density Functional Perturbation Theory (DPFT), where a 2 3 2 3 2 supercell consisting of 192 atoms, an energy cutoff of 750 eV and a k-point mesh including the G-point only was used. XRD-patterns were calculated in the software CrystalDiffractH for Windows 1.4.5. using a simulated wavelength of Cu, l 5 1.54.

Figure 11 | Radial distribution function (RDF) and angle distribution function (ADF) of R3-carbon phase, GC under 8.48 GPa, 30.3 GPa, and 1. Miller, E. D., Nesting, D. C. & Badding, J. V. Quenchable Transparent Phase of 58.3 GPa from our DFT simulations. Carbon. Chem. Mater. 9, 18–22 (1997).

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2. Ergun, S. & Tiensuu, V. H. Alicyclic Structures in . Nature 183, 1668–1670 35. Sternberg, M., Zapol, P. & Curtiss, L. A. Carbon Dimers on the Diamond (100) (1959). Surface: Growth and Nucleation. Phys. Rev. B 68, 205330 (2003). 3. Jenkins, G. M. & Kawamura, K. Structure of Glassy Carbon. Nature 231, 175–176 36. Gilkes, K. W. R., Gaskell, P. H. & Robertson, J. Comparison of Neutron-scattering (1971). Data for Tetrahedral Amorphous Carbon with Structural Models. Phys. Rev. B 51, 4. Pesin, L. A. Review Structure and Properties of Glass-like Carbon. J. Mater. Sci. 37, 12303–12312 (1995). 1–28 (2002). 37. Raoux, S., Welnic, W. & Ielmini, D. Phase Change Materials and Their 5. Pesin, L. A. & Baitinger, E. M. A New Structural Model of Glass-like Carbon. Application to Nonvolatile Memories. Chem. Rev. 110, 240–267 (2009). Carbon 40, 295–306 (2002). 38. Kolobov, A. V., Krbal, M., Fons, P., Tominaga, J. & Uruga, T. Distortion-triggered 6. Harris, P. J. F. Fullerene-related Structure of Commercial Glassy . Philos. Loss of Long-range Order in Solids with Bonding Energy Hierarchy. Nat. Chem. 3, Mag. 84, 3159–3167 (2004). 311–316 (2011). 7. Mao, W. L. et al. Bonding Changes in Compressed Superhard Graphite. Science 39. Johnson, W. L. Thermodynamic and Kinetic Aspects of the Crystal to Glass 302, 425–427 (2003). Transformation in Metallic Materials. Prog. Mater. Sci. 30, 81–134 (1986). 8. Iwasa, Y. et al. New Phases of C60 Synthesized at High Pressure. Science 264, 1570– 40. Rehn, L. E., Okamoto, P. R., Pearson, J., Bhadra, R. & Grimsditch, M. Solid-State 1572 (1994). Amorphization of Zr3Al: Evidence of an Elastic Instability and First-Order Phase 9. Sundqvist, B. Fullerenes under High Pressures. Adv. Phys. 48, 1–134 (1999). Transformation. Phys. Rev. Lett. 59, 2987–2990 (1987). 10. Li, Q. et al. Superhard Monoclinic Polymorph of Carbon. Phys. Rev. Lett. 102, 41. Fecht, H. J. Defect-induced Melting and Solid-state Amorphization. Nature 356, 175506 (2009). 133–135 (1992). 11. Umemoto, K., Wentzcovitch, R. M., Saito, S. & Miyake, T. Body-Centered 42. Lyapin, A. G. & Brazhkin, V. V. Pressure-induced Lattice Instability and Solid- Tetragonal C : A Viable sp3 Carbon Allotrope. Phys. Rev. Lett. 104, 125504 (2010). 4 state Amorphization. Phys. Rev. B 54, 12036–12048 (1996). 12. Wang, J. T., Chen, C. f. & Kawazoe, Y. Low-Temperature Phase Transformation from Graphite to sp3 Orthorhombic Carbon. Phys. Rev. Lett. 106, 075501 (2011). 43. Vadim, V. B. et al. Bulk Nanostructured Carbon Phases Prepared from C60: 13. Niu, H. et al. Families of Superhard Crystalline Carbon Allotropes Constructed via Approaching the ‘Ideal’ Hardness. J Phys.: Conden. Matt. 19, 236209 (2007). Cold Compression of Graphite and Nanotubes. Phys. Rev. Lett. 108, 135501 44. Brazhkin, V. V., Lyapin, A. G. & Hemley, R. J. Harder than Diamond: Dreams and (2012). Reality. Philos. Mag. A 82, 231–253 (2002). 45. Jiang, X., Zhao, J. J., Wu, A. M., Bai, Y. Z. & Jiang, X. Mechanical and Electronic 14. Zhao, Z. S. et al. Novel Superhard Carbon: C-Centered Orthorhombic C8. Phys. Rev. Lett. 107, 215502 (2011). Properties of B12-based Ternary Crystals of Orthorhombic Phase. J. Phys.: 15. Wang, Y., Panzik, J. E., Kiefer, B. & Lee, K. K. M. of Graphite Conden. Matt. 22, 315503 (2010). under Room-temperature Compression and Decompression. Sci. Rep. 2, 520 46. Jiang, X., Zhao, J. & Jiang, X. Correlation Between Hardness and Elastic Moduli of (2012). the Covalent Crystals. Comp. Mater. Sci. 50, 2287–2290 (2011). 16. Bundy, F. P. Direct Conversion of Graphite to Diamond in Static Pressure 47. Kresse, G. & Furthmu¨ller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Apparatus. Science 137, 1057–1058 (1962). Calculations Using a Plane-wave Basis Set. Phys. Rev. B 54, 11169-11186 (1996). 17. Irifune, T., Kurio, A., Sakamoto, S., Inoue, T. & Sumiya, H. Materials: Ultrahard 48. Blo¨chl, P. E. Projector Augmented-wave Method. Phys. Rev. B 50, 17953–17979 polycrystalline diamond from graphite. Nature 421, 599–600 (2003). (1994). 18. Lin, Y. et al. Amorphous Diamond: A High-Pressure Superhard Carbon 49. Perdew, J. P. et al. Restoring the Density-Gradient Expansion for Exchange in Allotrope. Phys. Rev. Lett. 107, 175504 (2011). Solids and Surfaces. Phys. Rev. Lett. 100, 136406 (2008). 19. Wallace, D. C. Evaluation of Thermodynamic Functions of Elemental Crystals 50. Zhao, J., Winey, J. M. & Gupta, Y. M. First-principles Calculations of Second- and and Liquids. Phys. Rev. E 56, 1981–1986 (1997). Third-order Elastic Constants for Single Crystals of Arbitrary Symmetry. Phys. 20. Holmstro¨m, E. et al. Ab Initio Method for Locating Characteristic Potential- Rev. B 75, 094105 (2007). energy Minima of Liquids. Phys. Rev. E 80, 051111 (2009). 51. Hill, R. The Elastic Behaviour of a Crystalline Aggregate. Proc. Phys. Soc. A 65,349 21. Ame´zaga, A. et al. Quantitative Local Environment Characterization in (1952). Amorphous Oxides. Phys. Rev. B 81, 014210 (2010). 52. Togo, A., Oba, F. & Tanaka, I. First-principles Calculations of the Ferroelastic 22. Bock, N. et al. Liquid-state Properties from First-principles Density Functional Transition between Rutile-type and CaCl2-type SiO2 at High Pressures. Phys. Rev. Theory Calculations: Static Properties. Phys. Rev. B 82, 144101 (2010). B 78, 134106 (2008). 23. Holmstro¨m, E. et al. Structure Discovery for Metallic using Stochastic 53. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized Gradient Approximation Quenching. Phys. Rev. B 82, 024203 (2010). Made Simple. Phys. Rev. Lett. 77, 3865–3868 (1996). 24. A˚ rhammar, C. et al. Unveiling the Complex Electronic Structure of Amorphous Metal Oxides. P. Nat. Acad. Sci. Usa. 108, 6355–6360 (2011). 25. Grimme, S. Semiempirical GGA-type Density Functional Constructed with a Long-range Dispersion Correction. J. Comput. Chem. 27, 1787–1799 (2006). 26. Dion, M., Rydberg, H., Schro¨der, E., Langreth, D. C. & Lundqvist, B. I. Van der Acknowledgements Waals Density Functional for General Geometries. Phys. Rev. Lett. 92, 246401 We would like to acknowledge the Swedish Research Council (VR and FORMAS) and (2004). Stiftelsen J. Gust Richerts Minne (SWECO) for financial support. X. Jiang and P. Liu are thankful to the China scholarship council (CSC). R. Ahuja would like to acknowledge the 27. Klimesˇ, J., Bowler, D. R. & Michaelides, A. Van der Waals Density Functionals ˚ Applied to Solids. Phys. Rev. B 83, 195131 (2011). Wenner-gren Foundation for financial support. C. Arhammar would like to thank Prof. 28. Townsend, S. J., Lenosky, T. J., Muller, D. A., Nichols, C. S. & Elser, V. Negatively Duane Wallace et al. LANL, U.S.A. for the theoretical development of the SQ-method. SNIC Curved Graphitic Sheet Model of Amorphous Carbon. Phys. Rev. Lett. 69, 921– and UPPMAX are acknowledged for providing computing time. 924 (1992). 29. Marks, N. A. et al. Comparison of Density-functional, Tight-binding, and Author contributions Empirical Methods for the Simulation of Amorphous Carbon. Phys. Rev. B 65, X.J. and C.A˚ . wrote the main manuscript text and prepared the figures. J.Z. and R.A. have 075411 (2002). analyzed the results. X.J., C.A., L.P., J.Z. and R.A. have discussed & reviewed the manuscript. 30. Marks, N. A., McKenzie, D. R., Pailthorpe, B. A., Bernasconi, M. & Parrinello, M. Ab Initio Simulations of Tetrahedral Amorphous Carbon. Phys. Rev. B 54, 9703–9714 (1996). Additional information 31. Kittel, C. Introduction to Solid State Physics. (Wiley, 1996). Competing financial interests: The authors declare no competing financial interests. 32. Mackay, A. L. & Terrones, H. Diamond from Graphite. Nature 352, 762–762 (1991). License: This work is licensed under a Creative Commons 33. Stephan, U., Frauenheim, T., Blaudeck, P. & Jungnickel, G. p Bonding versus Attribution-NonCommercial-NoDerivs 3.0 Unported License. To view a copy of this Electronic-defect Generation: An Examination of Band-gap Properties in license, visit http://creativecommons.org/licenses/by-nc-nd/3.0/ Amorphous Carbon. Phys. Rev. B 50, 1489–1501 (1994). How to cite this article: Jiang, X., A˚ rhammar, C., Peng, L., Zhao, J. & Ahuja, R. The 34. Goyette, A. N. et al. Spectroscopic Determination of Carbon Dimer Densities in R3-carbon allotrope: a pathway towards glassy carbon under high pressure. Sci. Rep. 3, Plasmas. J. Phys. D. Appl. Phys. 31, 1975 (1998). 1877; DOI:10.1038/srep01877 (2013).

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